# Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography

## Abstract

Magnetic resonance electrical impedance tomography visualizes current density and/or conductivity distributions inside an electrically conductive object. Injecting currents into the imaging object along at least two different directions, induced magnetic flux density data can be measured using a magnetic resonance imaging scanner. Without rotating the object inside the scanner, we can measure only one component of the magnetic flux density denoted as B{sub z}. Since the biological tissues such as skeletal muscle and brain white matter show strong anisotropic properties, the reconstruction of anisotropic conductivity tensor is indispensable for the accurate observations in the biological systems. In this paper, we propose a direct method to reconstruct an axial apparent orthotropic conductivity tensor by using multiple B{sub z} data subject to multiple injection currents. To investigate the anisotropic conductivity properties, we first recover the internal current density from the measured B{sub z} data. From the recovered internal current density and the curl-free condition of the electric field, we derive an over-determined matrix system for determining the internal absolute orthotropic conductivity tensor. The over-determined matrix system is designed to use a combination of two loops around each pixel. Numerical simulations and phantom experimental results demonstrate that the proposed algorithm stably determines themore »

- Authors:

- Department of Biomedical Engineering, Kyung Hee University, Yongin, Gyeonggi (Korea, Republic of)
- Department of Mathematics, Konkuk University, Seoul (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 22399264

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Physics; Journal Volume: 117; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; ANISOTROPY; COMPUTERIZED SIMULATION; CURRENT DENSITY; ELECTRIC CONDUCTIVITY; ELECTRIC CURRENTS; ELECTRIC FIELDS; FLUX DENSITY; IMPEDANCE; MAGNETIC FLUX; MAGNETIC RESONANCE; NMR IMAGING; PHANTOMS; TENSORS; TOMOGRAPHY

### Citation Formats

```
Sajib, Saurav Z. K., Kim, Ji Eun, Jeong, Woo Chul, Kim, Hyung Joong, Woo, Eung Je, and Kwon, Oh In, E-mail: oikwon@konkuk.ac.kr.
```*Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography*. United States: N. p., 2015.
Web. doi:10.1063/1.4914904.

```
Sajib, Saurav Z. K., Kim, Ji Eun, Jeong, Woo Chul, Kim, Hyung Joong, Woo, Eung Je, & Kwon, Oh In, E-mail: oikwon@konkuk.ac.kr.
```*Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography*. United States. doi:10.1063/1.4914904.

```
Sajib, Saurav Z. K., Kim, Ji Eun, Jeong, Woo Chul, Kim, Hyung Joong, Woo, Eung Je, and Kwon, Oh In, E-mail: oikwon@konkuk.ac.kr. Sat .
"Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography". United States.
doi:10.1063/1.4914904.
```

```
@article{osti_22399264,
```

title = {Reconstruction of apparent orthotropic conductivity tensor image using magnetic resonance electrical impedance tomography},

author = {Sajib, Saurav Z. K. and Kim, Ji Eun and Jeong, Woo Chul and Kim, Hyung Joong and Woo, Eung Je and Kwon, Oh In, E-mail: oikwon@konkuk.ac.kr},

abstractNote = {Magnetic resonance electrical impedance tomography visualizes current density and/or conductivity distributions inside an electrically conductive object. Injecting currents into the imaging object along at least two different directions, induced magnetic flux density data can be measured using a magnetic resonance imaging scanner. Without rotating the object inside the scanner, we can measure only one component of the magnetic flux density denoted as B{sub z}. Since the biological tissues such as skeletal muscle and brain white matter show strong anisotropic properties, the reconstruction of anisotropic conductivity tensor is indispensable for the accurate observations in the biological systems. In this paper, we propose a direct method to reconstruct an axial apparent orthotropic conductivity tensor by using multiple B{sub z} data subject to multiple injection currents. To investigate the anisotropic conductivity properties, we first recover the internal current density from the measured B{sub z} data. From the recovered internal current density and the curl-free condition of the electric field, we derive an over-determined matrix system for determining the internal absolute orthotropic conductivity tensor. The over-determined matrix system is designed to use a combination of two loops around each pixel. Numerical simulations and phantom experimental results demonstrate that the proposed algorithm stably determines the orthotropic conductivity tensor.},

doi = {10.1063/1.4914904},

journal = {Journal of Applied Physics},

number = 10,

volume = 117,

place = {United States},

year = {Sat Mar 14 00:00:00 EDT 2015},

month = {Sat Mar 14 00:00:00 EDT 2015}

}